Menu Close

Category: Limits

Question-133454

Question Number 133454 by rs4089 last updated on 22/Feb/21 Answered by TheSupreme last updated on 22/Feb/21 $$\Omega=\left\{\left({x},{y}\right)\mid\:{x}>\mathrm{0}\:;\:\mathrm{0}<{y}<{x}\right\} \\ $$$$\Omega=\left\{\left({x},{y}\right)\mid\:{y}>\mathrm{0},\:{x}>{y}\right\} \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{{x}} {e}^{−{xy}}…

a-0-x-a-n-1-1-1-a-n-Find-possible-value-for-x-such-that-a-n-1-for-some-n-N-For-example-x-2-a-1-1-x-3-2-a-2-1-x-if-a-n-1-

Question Number 2322 by prakash jain last updated on 15/Nov/15 $${a}_{\mathrm{0}} ={x} \\ $$$${a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{1}+{a}_{{n}} } \\ $$$$\mathrm{Find}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{for}\:{x}\:\mathrm{such}\:\mathrm{that} \\ $$$${a}_{{n}} =−\mathrm{1}\:\mathrm{for}\:\mathrm{some}\:{n}\in\mathbb{N}. \\ $$$$\mathrm{For}\:\mathrm{example}:\: \\ $$$${x}=−\mathrm{2},\:{a}_{\mathrm{1}}…

use-weierstrass-m-test-and-dirichlet-test-to-confirm-the-uniformly-covergence-of-the-following-series-in-the-interval-0-1-a-n-1-cosnx-n-4-b-n-1-cosnx-n-8-7-c-n-1-

Question Number 133277 by Engr_Jidda last updated on 20/Feb/21 $${use}\:{weierstrass}\:{m}−{test}\:{and}\:{dirichlet} \\ $$$${test}\:{to}\:{confirm}\:{the}\:{uniformly}\:{covergence} \\ $$$${of}\:{the}\:{following}\:{series}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.{a}\right)\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosnx}}{{n}^{\mathrm{4}} } \\ $$$$\left.{b}\right)\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosnx}}{{n}^{\frac{\mathrm{8}}{\mathrm{7}}} } \\…

lim-x-x-2-x-x-1-4-sin-2-x-x-2-sin-3x-

Question Number 133114 by bemath last updated on 19/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\right)^{\mathrm{x}^{\mathrm{2}} +\mathrm{sin}\:\mathrm{3x}} ? \\ $$ Answered by bobhans last updated on 19/Feb/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{{x}^{\mathrm{2}}…

advanced-calculus-evaluation-k-2-1-k-k-1-k-k-2-1-k-k-1-k-k-2-1-k-k-n-2-1-n-k-

Question Number 133068 by mnjuly1970 last updated on 18/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}…..{calculus}…. \\ $$$$\:\:\:{evaluation}::\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \left(\:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}}\right) \\ $$$$\:\:\:\::::\boldsymbol{\Phi}=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}} \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\underset{{n}=\mathrm{2}}…